Add-on UI won't display!
OK, so I figured it out! 

The poll() function was cutting out my UI, because it was checking if something was selected before allowing my addon to run, and I was deleting my selected object at the end of my execute() function.

Therefore, to fix it I simply selected one of the newly created objects (the original code creates several new objects) and THEN unlinked the original object. So something is always selected, therefore, poll() thinks the context is still correct, therefore letting my UI to continue displaying.